This is a review for the entire John Byrne era, not just this volume.
Look... I appreciate what John Byrne did for the Superman mythos. The Man of Steel miniseries is perfectly enjoyable in its own way, and I'm grateful that it cleaned up Superman continuity a bit for the modern age. But Byrne's actual ongoing run (alongside Marv Wolfman and others) is just a slog. He never commits to any particular plotline. Every subplot runs at a glacial pace, popping up for one or two pages at random in every issue. The main plots are dreadfully generic and cliche. This is in that weird, brief era when Superman was freed from the chains of the Silver Age, but hadn't been elevated to his fullest potential by writers like Joe Kelly, Kurt Busiek, Jeph Loeb, Grant Morrison, or even Mark Millar. Because of that it's... pretty rough. There's just nothing to get attached to. Every once in a while there's a fun story, but it's surrounded by forgettable filler, mindless action, and a truly offensive amount of intrusive expositional thought bubbles. You can't even enjoy the first appearances (Post-Crisis) of several Superman villains on their own, because they're buried in irrelevant and uninteresting subplots. Tell me, who seriously cares about Jerry White? Or Cat Grant? Gangbuster? The Circle? The Manhunters? The voodoo killer? Brainiac?
Oh what's that? You DO care about Brainiac? You fool. You absolute idiot. When I said "Brainiac", you probably thought I was talking about the genocidal, planet-destroying, city-bottling, body-swapping, alien robot who is among Superman's greatest foes. No, silly. I'm obviously talking about the short, fat, mentally unstable illusionist with psychic powers who may or may not be possessed by the distant extraterrestrial dismembodied consciousness of Sir Not-Appearing-in-This-Comic. You know. Brainiac. The iconic Brainiac. Everyone's favorite. What were you expecting? Thanks John.
Do I even need to mention the story where Superman and Barda are brainwashed by an alien named Sleez into filming a porno? That's a real thing that happens.
Oh, and the worst part of this run? Byrne doesn't even finish any of his own plotlines! To see the conclusions to any of the subplots contained in the four Man of Steel Omnibuses, you'll have to check out "Superman: The Exile and Other Stories Omnibus", where Roger Stern and Jerry Orway clean up Byrne's mess and try to resolve it all (and it's actually better, incidentally). This series really just isn't worth your time. There are so many better Superman runs (like the woefully underrated "City of Tomorrow" era). Hell, even the Man of Steel miniseries, the only thing here with any substantial value, has been made completely obsolete by MULTIPLE superior origin comics like Birthright and Secret Origin.
In conclusion, only read this for the historical value. You won't find anything in these volumes that hasn't been done better elsewhere. Superman is a difficult character to write, and I don't envy any writer tasked with doing a long run with him, but I can only judge what's in front of me. And it's just not worth the time.